Question

fractions 1. which of the following inequalities is true for the fractions \\(\frac{2}{5}\\), \\(\frac{5}{13}\\), and \\(\frac{3}{7}\\)? a. \\(\frac{5}{13} < \frac{2}{5} < \frac{3}{7}\\) b. \\(\frac{5}{13} < \frac{3}{7} < \frac{2}{5}\\) c. \\(\frac{2}{5} < \frac{3}{7} < \frac{5}{13}\\) d. \\(\frac{2}{5} < \frac{5}{13} < \frac{3}{7}\\) to convert a fraction to a decimal, divide the numerator by the denominator. match each fraction with its decimal equivalent. you may need to round. 0.38 0.4 0.43 \\(\frac{2}{5}\\) =

Explanation:

Step1: Convert each fraction to decimal

• For $\frac{2}{5}$: Divide 2 by 5. $2\div5 = 0.4$
• For $\frac{5}{13}$: Divide 5 by 13. $5\div13\approx0.38$ (rounded to two decimal places)
• For $\frac{3}{7}$: Divide 3 by 7. $3\div7\approx0.43$ (rounded to two decimal places)

Step2: Compare the decimals

Now we have the decimals: $\frac{2}{5}=0.4$, $\frac{5}{13}\approx0.38$, $\frac{3}{7}\approx0.43$

Comparing these decimals: $0.38 < 0.4 < 0.43$, which means $\frac{5}{13} < \frac{2}{5} < \frac{3}{7}$? Wait, no, wait. Wait, $\frac{5}{13}\approx0.38$, $\frac{2}{5}=0.4$, $\frac{3}{7}\approx0.43$. So the order from smallest to largest is $\frac{5}{13} \approx 0.38$, $\frac{2}{5}=0.4$, $\frac{3}{7}\approx0.43$. Wait, but let's check the options:

Option A: $\frac{5}{13} < \frac{2}{5} < \frac{3}{7}$? Wait, $\frac{5}{13}\approx0.38$, $\frac{2}{5}=0.4$, so $0.38 < 0.4$, then $\frac{2}{5}=0.4 < \frac{3}{7}\approx0.43$. So $\frac{5}{13} < \frac{2}{5} < \frac{3}{7}$? Wait, but let's check the options again.

Wait the options are:

A. $\frac{5}{13} < \frac{2}{5} < \frac{3}{7}$

B. $\frac{5}{13} < \frac{3}{7} < \frac{2}{5}$

C. $\frac{2}{5} < \frac{3}{7} < \frac{5}{13}$

D. $\frac{2}{5} < \frac{5}{13} < \frac{3}{7}$

Wait, no, I think I made a mistake. Wait $\frac{2}{5}=0.4$, $\frac{5}{13}\approx0.38$, so $\frac{5}{13}\approx0.38$ is less than $\frac{2}{5}=0.4$. Then $\frac{3}{7}\approx0.43$ is greater than $\frac{2}{5}=0.4$. So the correct order is $\frac{5}{13} \approx 0.38 < \frac{2}{5}=0.4 < \frac{3}{7}\approx0.43$, which is $\frac{5}{13} < \frac{2}{5} < \frac{3}{7}$, which is option A? Wait no, wait the options:

Wait the options are:

A. $\frac{5}{13} < \frac{2}{5} < \frac{3}{7}$

B. $\frac{5}{13} < \frac{3}{7} < \frac{2}{5}$

C. $\frac{2}{5} < \frac{3}{7} < \frac{5}{13}$

D. $\frac{2}{5} < \frac{5}{13} < \frac{3}{7}$

Wait, let's recalculate the decimals more accurately.

$\frac{2}{5}=0.4$ exactly.

$\frac{5}{13}$: 5 divided by 13. 130.38 = 4.94, 130.3846 = 5, so $\frac{5}{13}\approx0.3846$

$\frac{3}{7}$: 3 divided by 7. 7*0.42857 = 3, so $\frac{3}{7}\approx0.42857$

So now, $\frac{5}{13}\approx0.3846$, $\frac{2}{5}=0.4$, $\frac{3}{7}\approx0.42857$

So comparing: 0.3846 < 0.4 < 0.42857, which is $\frac{5}{13} < \frac{2}{5} < \frac{3}{7}$, which is option A? Wait but let's check the options again. Wait the options:

A. $\frac{5}{13} < \frac{2}{5} < \frac{3}{7}$

Yes, that's correct. Wait but let's check the other options.

Option B: $\frac{5}{13} < \frac{3}{7} < \frac{2}{5}$: But $\frac{3}{7}\approx0.42857$ is greater than $\frac{2}{5}=0.4$, so this is wrong.

Option C: $\frac{2}{5} < \frac{3}{7} < \frac{5}{13}$: $\frac{2}{5}=0.4$ is less than $\frac{3}{7}\approx0.42857$, but $\frac{3}{7}\approx0.42857$ is greater than $\frac{5}{13}\approx0.3846$, so this is wrong.

Option D: $\frac{2}{5} < \frac{5}{13} < \frac{3}{7}$: $\frac{2}{5}=0.4$ is greater than $\frac{5}{13}\approx0.3846$, so this is wrong.

So the correct answer is option A.

Answer:

A. $\frac{5}{13} < \frac{2}{5} < \frac{3}{7}$